CN108008361B - Distributed MIMO radar interference waveform design method based on radio frequency stealth - Google Patents

Distributed MIMO radar interference waveform design method based on radio frequency stealth Download PDF

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CN108008361B
CN108008361B CN201711082783.2A CN201711082783A CN108008361B CN 108008361 B CN108008361 B CN 108008361B CN 201711082783 A CN201711082783 A CN 201711082783A CN 108008361 B CN108008361 B CN 108008361B
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interference
radar
distributed mimo
mimo radar
radio frequency
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时晨光
汪飞
李海林
周建江
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Nanjing University of Aeronautics and Astronautics
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/38—Jamming means, e.g. producing false echoes

Abstract

The invention discloses a distributed MIMO radar interference waveform design method based on radio frequency stealth, which comprises the steps of firstly, under the condition that an onboard electronic interference system and a distributed MIMO radar are subjected to electronic countermeasure, acquiring frequency response of a target relative to the distributed MIMO radar, a radar emission signal and a receiver noise power spectrum according to priori knowledge; then, establishing a distributed MIMO radar interference waveform design model based on radio frequency stealth by taking the total transmitting power of the minimum airborne electronic interference system as a target, and solving the model by a Lagrange multiplier method; and (4) selecting the interference waveform with the minimum total transmission power of the airborne electronic interference system as an optimal solution through dichotomy iterative calculation, so as to obtain the minimum interference total power which meets the constraint condition. The invention achieves the following beneficial effects: the method not only ensures the interference performance of the distributed MIMO radar system, but also effectively improves the radio frequency stealth performance of the airborne electronic interference system.

Description

Distributed MIMO radar interference waveform design method based on radio frequency stealth
Technical Field
The invention relates to a distributed MIMO radar interference waveform design method based on radio frequency stealth, and belongs to the technical field of radar interference waveform design.
Background
The distributed MIMO radar system is an organic whole which consists of a plurality of transmitting antennas and a plurality of receiving antennas, is mutually cooperated and closely associated, realizes the cooperative work of a time domain, a frequency domain and a space domain, and completes the functions of reconnaissance and detection, information collection, identification and tracking, interference suppression, firepower guidance and the like of a target. Targets in the same field of view may be detected by multiple transmit and receive antennas. In order to prevent the distributed MIMO radar from detecting and tracking the target, it is not enough to interfere with only part of radar receivers in the system, and all the radar receivers must be effectively interfered to shield the target. The interference resources of the airborne electronic interference system are often limited, and in order to achieve the optimal interference effect, the interference emission waveform needs to be reasonably designed.
There are two main criteria for the design of the radar interference waveform in common use: firstly, Signal to Interference plus Noise Ratio (SINR) is minimized to reduce target detection performance of the radar system; and secondly, Mutual Information (MI) between radar receiving echoes and target impulse responses is minimized, so that the target parameter estimation performance of the radar system is reduced.
However, the increasingly advanced passive detection system can accurately detect, locate, sort and identify the radio frequency signals transmitted by the electronic jammers by intercepting and processing the radio frequency signals, and poses a serious threat to the battlefield viability of the own onboard electronic jammer system. The radio frequency stealth technology can obviously reduce the probability that the active radiation system is intercepted, found, sorted and identified by an enemy passive detection system and attacked by an anti-radiation missile by controlling the radiation energy, waveform parameters and other methods of the active radiation system, thereby improving the battlefield viability and the penetration resistance of the active radiation system and a carrying platform thereof.
At present, the research on radio frequency stealth technology mainly focuses on the field of radar and communication systems, and no public report is found for active suppressive interference of distributed MIMO radar. The existing research on active suppressive interference mainly aims at maximizing interference efficiency, but increases the interception probability of an enemy passive detection system on interference signals while increasing the transmission power of the interference system, thereby greatly reducing the radio frequency stealth performance of the interference system. Therefore, the problem of designing interference waveforms of distributed MIMO radar based on radio frequency stealth needs to be researched.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to provide a distributed MIMO radar interference waveform design method based on radio frequency stealth, which can minimize the total transmission power of an airborne electronic interference system and improve the radio frequency stealth performance of the airborne electronic interference system through interference waveform optimization design.
In order to achieve the above object, the present invention adopts the following technical solutions:
a distributed MIMO radar interference waveform design method based on radio frequency stealth is characterized by comprising the following steps:
1) according to the priori knowledge, determining target frequency response, MIMO radar transmitting signals and a radar receiver noise power spectrum, and determining radiation parameters and interference performance MI threshold parameters of an interference system;
2) the method comprises the steps that a distributed MIMO radar interference waveform design model based on radio frequency stealth is established under the condition that the total transmitting power of an airborne electronic interference system is minimized and certain interference performance is met;
3) solving the model by a Lagrange multiplier method to meet the interference performance threshold deltaMIDetermining an optimal solution of a Lagrange multiplier under the condition of the minimum interference total power;
4) substituting the optimal solution obtained in the step 3) into a necessary condition of a Carlo-Couin-Tack condition to obtain an optimal interference emission waveform of the distributed MIMO radar, thereby forming a distributed MIMO radar interference waveform design scheme.
The method for designing the interference waveform of the distributed MIMO radar based on the radio frequency stealth is characterized in that the specific content in the step 1) is as follows:
acquiring a distributed MIMO radar transmitting signal matrix S, the frequency response h of a target relative to a radar system, and the noise n at a radar receiver as prior knowledge; wherein S ═ S1,S2,…,SN]N is the number of transmitting antennas of the distributed MIMO radar, and the transmitting signal S of the ith antenna in the systemiAn M multiplied by L dimension Toeplitz matrix is adopted, M is the radar echo signal length, L is the target frequency response length, and M is equal to NL; the frequency response h of the target relative to the radar is a zero-mean complex Gaussian random vector and meets the requirement
Figure GDA0002902809560000021
Wherein xihA target frequency response covariance matrix; the noise n at the radar receiver is a zero-mean complex Gaussian random vector and meets the requirements
Figure GDA0002902809560000022
Wherein xinIs a noise covariance matrix.
The method for designing the interference waveform of the distributed MIMO radar based on the radio frequency stealth is characterized in that the specific content in the step 2) is as follows:
MI threshold delta according to the interference performance given in advanceMIEstablishing a distributed MIMO radar optimal interference waveform design mathematical model based on radio frequency stealth:
Figure GDA0002902809560000023
in the formula, the upper label (·)HRepresenting the conjugate transpose of the matrix, the interference signal J is a zero-mean complex Gaussian random vector, and satisfies
Figure GDA0002902809560000024
Wherein xiJIs an interference covariance matrix.
The method for designing the interference waveform of the distributed MIMO radar based on the radio frequency stealth is characterized in that eigenvalue decomposition is adopted after the processing in the step 2), and a covariance matrix xi is adoptedh、ΞJ、ΞnCan be decomposed respectively as follows:
Figure GDA0002902809560000025
in the formula of Uh、UJAnd UnRespectively unitary matrix and diagonal matrix Lambdah＝diag[λ1,…,λNL]，
Figure GDA0002902809560000031
Wherein λ isi、
Figure GDA0002902809560000032
And
Figure GDA0002902809560000033
respectively are eigenvalues of corresponding diagonal matrixes; through matrix operation, the mathematical model is converted into:
Figure GDA0002902809560000034
in the formula (I), the compound is shown in the specification,
Figure GDA0002902809560000035
is the eigenvalue of the radar transmit signal matrix S.
The method for designing the interference waveform of the distributed MIMO radar based on the radio frequency stealth is characterized in that the step 3) specifically comprises the following steps:
31) introducing Lagrange multiplier xi to construct Lagrange multiplier
Figure GDA0002902809560000036
32) Designing solvable nonlinear equations
Figure GDA0002902809560000037
Optimized caroneed-kuen-tower conditions:
33) and determining the Lagrangian multiplier under the optimized Carlo-Cohn-Tak condition by adopting a dichotomy iterative calculation.
The method for designing the interference waveform of the distributed MIMO radar based on the radio frequency stealth is characterized in that the step 32) comprises the following steps:
will be described in the above formula
Figure GDA0002902809560000038
Are respectively paired
Figure GDA00029028095600000313
The first partial derivative is calculated with xi and let:
Figure GDA0002902809560000039
at the same time satisfy
Figure GDA00029028095600000310
The KKT requirement for the nonlinear optimization solution is as follows:
Figure GDA00029028095600000311
wherein, variables marked with "+" respectively represent the optimal solution of each parameter.
The method for designing the interference waveform of the distributed MIMO radar based on radio frequency stealth is characterized in that the specific content of the step 33) is as follows:
by solving equation (2), the optimal interference waveform of the airborne electronic interference system
Figure GDA00029028095600000312
Can be expressed as:
Figure GDA0002902809560000041
ξ*is a constant whose magnitude depends on a given MI threshold:
Figure GDA0002902809560000042
through dichotomy iterative computation, xi satisfying the formula (4)*The value is substituted into the formula (3) to obtain a group of interference waveforms which minimize the total transmitting power of the airborne electronic interference system
Figure GDA0002902809560000043
And finally determining the total interference power of the system.
The invention achieves the following beneficial effects:
1) the method mainly aims at the situation that the airborne electronic jammers and the distributed MIMO radar are subjected to electronic countermeasure in the actual battlefield, and takes the minimum system interference total power as a target to perform self-adaptive optimization design on the transmission waveform of the airborne electronic jammers under the condition of meeting certain interference performance on the basis of acquiring the frequency response of the target relative to the distributed MIMO radar, the radar transmission signal and the noise power spectrum according to the priori knowledge;
2) on the basis of obtaining the frequency response of a target relative to a distributed MIMO radar, a radar emission signal and a noise power spectrum, the method takes the total emission power of a minimized airborne electronic interference system as a target, and establishes a distributed MIMO radar interference waveform design model based on radio frequency stealth under the condition of meeting a certain interference performance, so that the interference performance of the distributed MIMO radar system is ensured, and the airborne electronic interference system has the optimal radio frequency stealth performance;
3) compared with the prior art, the method not only ensures the interference performance of the distributed MIMO radar system, but also effectively improves the radio frequency stealth performance of the airborne electronic interference system.
Drawings
Fig. 1 is a distributed MIMO radar interference model;
FIG. 2 is a flow diagram of a distributed MIMO radar interference waveform design;
FIG. 3 is a distributed MIMO radar transmit signal spectrum, a target frequency response power spectrum, and a noise power spectrum;
FIG. 4 is a distributed MIMO radar interference waveform design result;
fig. 5 is a graph of interference total power in different interference waveform design methods.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
Firstly, under the condition that an onboard electronic interference system and a distributed MIMO radar are subjected to electronic countermeasure, acquiring frequency response of a target relative to the distributed MIMO radar, a radar transmitting signal and a receiver noise power spectrum according to priori knowledge; and then, establishing a distributed MIMO radar interference waveform design model based on radio frequency stealth by taking the total transmitting power of the minimum airborne electronic interference system as a target under the condition of meeting certain interference performance, and solving the model by a Lagrange multiplier method. Through dichotomy iterative calculation, selecting an interference waveform which enables the total transmitting power of the airborne electronic interference system to be minimum under the condition of meeting certain interference performance
Figure GDA0002902809560000051
As an optimal solution, transmitting the optimal interference waveform
Figure GDA0002902809560000052
The minimum interference total power which meets the constraint condition can be obtained by substituting the necessary condition of the Karaoke-Cohn-Tack condition (KKT).
The specific method comprises the following steps:
1) determining a target frequency response and MIMO radar transmission signals:
by using a priori knowledge of radar transmission signals, target frequency response, receiver noise and the like, a distributed MIMO radar interference model is assumed as shown in FIG. 1.
Determining parameters such as radiation parameters and interference performance MI thresholds of an interference system: according to the requirement of radio frequency stealth performance, the length of a radar echo signal is assumed to be NL, and the additive white Gaussian noise power at a radar receiver is assumed to be NL
Figure GDA0002902809560000053
Calculating an interference performance threshold delta from a given MIMI。
2) The method comprises the steps that a distributed MIMO radar interference waveform design model based on radio frequency stealth is established under the condition that the total transmitting power of an airborne electronic interference system is minimized and certain interference performance is met;
according to the requirement of an airborne electronic interference system on the interference performance of the distributed MIMO radar, a distributed MIMO radar optimal interference waveform design mathematical model based on radio frequency stealth is established, and the mathematical model is as follows:
Figure GDA0002902809560000054
in the formula, the upper label (·)HRepresenting the conjugate transpose of the matrix. The interference signal J is assumed to be a zero-mean complex Gaussian random vector and satisfies
Figure GDA0002902809560000055
Wherein xiJIs an interference covariance matrix.
Using eigenvalue decomposition, covariance matrix xih、ΞJ、ΞnCan be decomposed respectively as follows:
Figure GDA0002902809560000056
in the formula of Uh、UJAnd UnRespectively unitary matrix and diagonal matrix Lambdah＝diag[λ1,…,λNL]，
Figure GDA0002902809560000057
Figure GDA0002902809560000058
Wherein λ isi、
Figure GDA0002902809560000059
And
Figure GDA00029028095600000510
respectively, the eigenvalues of the corresponding diagonal matrix.
Through matrix operation, the mathematical model in formula (1) can be converted into:
Figure GDA00029028095600000511
(2) in the formula (I), wherein,
Figure GDA00029028095600000512
is the eigenvalue of the radar transmit signal matrix S.
31) Introducing Lagrange multiplier xi to construct a Lagrange multiplier as shown in a formula (3)
Figure GDA00029028095600000513
And determining that an interference performance threshold delta is metMIMinimum interference total power of
Figure GDA00029028095600000514
Expression (c):
Figure GDA0002902809560000061
32) designing solvable nonlinear equations
Figure GDA0002902809560000062
Optimized KKT conditions: determining an optimal interference waveform for an airborne electronic jamming system
Figure GDA0002902809560000063
Will be described in the above formula
Figure GDA0002902809560000064
Are respectively paired
Figure GDA00029028095600000613
The first partial derivative is calculated with xi and let:
Figure GDA0002902809560000065
at the same time satisfy
Figure GDA0002902809560000066
The KKT requirement for the nonlinear optimization solution is as follows:
Figure GDA0002902809560000067
wherein, all variables marked with the mark represent the optimal solution of each parameter respectively.
33) Implementing a non-linear equation
Figure GDA0002902809560000068
The optimization solution of (2):
by solving equation (5), the optimal interference waveform of the airborne electronic interference system
Figure GDA0002902809560000069
Can be expressed as:
Figure GDA00029028095600000610
ξ*is a constant whose magnitude depends on a given MI threshold:
Figure GDA00029028095600000611
through dichotomy iterative computation, xi satisfying the formula (7)*The value is substituted into the formula (6) to obtain a group of interference waveforms which minimize the total transmitting power of the airborne electronic interference system
Figure GDA00029028095600000612
And finally determining the total interference power of the system.
4) Substituting the optimal solution obtained in the step 3) into a necessary condition of a Carlo-Couin-Tack condition (KKT) to obtain an optimal interference emission waveform of the distributed MIMO radar, thereby forming a distributed MIMO radar interference waveform design scheme.
An example is given here, in which it is assumed that the parameters in step 2 are as shown in table 1.
Table 1 simulation parameter settings
Figure GDA0002902809560000071
The spectrum of the signal transmitted by the distributed MIMO radar, the power spectrum of the target frequency response and the power spectrum of the noise are shown in fig. 3. The interference waveform design result for the distributed MIMO radar is shown in fig. 4.
The distributed MIMO radar interference waveform design method based on radio frequency stealth is an optimal interference waveform obtained through calculation according to MIMO radar emission signals, frequency response of a target relative to a radar and a noise power spectrum at a radar receiver. As can be seen from fig. 4, the emission waveform of the airborne electronic interference system is mainly determined by the MIMO radar emission signal, the frequency response of the target relative to the radar, and the radar receiver noise power spectrum, and the interference power is mainly allocated to the frequency band with large radar emission signal power and low receiver noise power. In order to minimize the total transmission power of an interference system on the premise of ensuring certain interference performance, the interference power distribution is carried out according to the water injection principle by the distributed MIMO radar interference waveform design method based on radio frequency stealth, namely, the maximum power is distributed at the frequency band corresponding to the maximum radar transmission signal power level and the minimum receiver noise power.
Fig. 5 shows the interference total power comparison under different interference waveform design methods. As can be seen from fig. 5, as the requirement for interference performance increases, the transmission power of the on-board electronic interference system increases gradually. In addition, the total interference power obtained by the optimal interference waveform design method is obviously less than that of the uniform power distribution interference waveform design method, so that the radio frequency stealth performance of the optimal interference waveform design method is superior to that of the uniform power distribution interference waveform design method, because the uniform power distribution interference waveform uniformly distributes the interference power on the whole frequency band under the condition of no prior knowledge about radar transmission signals, target frequency response, noise power spectrum of a radar receiver and the like, the uniform power distribution interference waveform has poorer radio frequency stealth performance.
According to the simulation result, the interference waveform design method of the distributed MIMO radar based on the radio frequency stealth is based on the frequency response of the target relative to the distributed MIMO radar, the radar emission signal and the receiver noise power spectrum obtained according to the priori knowledge, the total emission power of the airborne electronic interference system is minimized, the interference waveform is subjected to self-adaptive optimization design, and therefore the radio frequency stealth performance of the airborne electronic interference system is effectively improved under the condition that certain interference performance is guaranteed.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (5)

1. A distributed MIMO radar interference waveform design method based on radio frequency stealth is characterized by comprising the following steps:
1) according to the priori knowledge, determining target frequency response, MIMO radar transmitting signals and a radar receiver noise power spectrum, and determining radiation parameters and interference performance MI threshold parameters of an interference system;
2) the method comprises the steps that a distributed MIMO radar interference waveform design model based on radio frequency stealth is established under the condition that the total transmitting power of an airborne electronic interference system is minimized and certain interference performance is met;
3) solving the model by a Lagrange multiplier method to meet the interference performance threshold deltaMIDetermining an optimal solution of a Lagrange multiplier under the condition of the minimum interference total power;
4) substituting the optimal solution obtained in the step 3) into a necessary condition of a Carlo-Couin-Tack condition to obtain an optimal interference emission waveform of the distributed MIMO radar, thereby forming a distributed MIMO radar interference waveform design scheme;
the concrete contents of the step 1) are as follows:
acquiring a distributed MIMO radar transmitting signal matrix S, the frequency response h of a target relative to a radar system, and the noise n at a radar receiver as prior knowledge;
wherein S ═ S1,S2,…,SN]N is the number of transmitting antennas of the distributed MIMO radar, and the transmitting signal S of the ith antenna in the systemiAn M multiplied by L dimension Toeplitz matrix is adopted, M is the radar echo signal length, L is the target frequency response length, and M is equal to NL;
the frequency response h of the target relative to the radar is a zero-mean complex Gaussian random vector and meets the requirement
Figure FDA0002902809550000011
Wherein xihA target frequency response covariance matrix;
the noise n at the radar receiver is a zero-mean complex Gaussian random vector and meets the requirements
Figure FDA0002902809550000012
Wherein xinIs a noise covariance matrix;
the specific content of the step 2) is as follows:
MI threshold delta according to the interference performance given in advanceMIEstablishing a distributed MIMO radar optimal interference waveform design mathematical model based on radio frequency stealth:
Figure FDA0002902809550000013
in the formula INLExpressing the identity matrix of NL order, S expressing the radar emission matrix, superscript (. circle.)HRepresenting the conjugate transpose of the matrix, the interference signal J is a zero-mean complex Gaussian random vector, and satisfies
Figure FDA0002902809550000014
Wherein xiJIs an interference covariance matrix.
2. The method according to claim 1, wherein eigenvalue decomposition is adopted after the processing of the step 2), and a covariance matrix xi is adoptedh、ΞJ、ΞnCan be decomposed respectively as follows:
Figure FDA0002902809550000021
in the formula of Uh、UJAnd UnUnitary matrix and diagonal matrix respectively
Figure 2
，
Figure FDA0002902809550000022
Wherein λ isi、
Figure FDA0002902809550000023
And
Figure FDA0002902809550000024
respectively are eigenvalues of corresponding diagonal matrixes;
through matrix operation, the mathematical model is converted into:
Figure FDA0002902809550000025
in the formula (I), the compound is shown in the specification,
Figure FDA0002902809550000026
is the eigenvalue of the radar transmit signal matrix S.
3. The method for designing the interference waveform of the distributed MIMO radar based on the radio frequency stealth as claimed in claim 2, wherein the step 3) specifically comprises the following steps:
31) introducing Lagrange multiplier xi to construct Lagrange multiplier
Figure FDA0002902809550000027
32) Designing solvable nonlinear equations
Figure FDA0002902809550000028
Optimized caroneed-kuen-tower conditions:
33) and determining the Lagrangian multiplier under the optimized Carlo-Cohn-Tak condition by adopting a dichotomy iterative calculation.
4. The method as claimed in claim 3, wherein the step 32) includes the following steps:
will be described in the above formula
Figure FDA0002902809550000029
Are respectively paired
Figure FDA00029028095500000210
The first partial derivative is calculated with xi and let:
Figure FDA00029028095500000211
at the same time satisfy
Figure FDA00029028095500000212
The KKT requirement for the nonlinear optimization solution is as follows:
Figure FDA00029028095500000213
wherein, the symbol is markedThe variables represent the optimal solutions for the respective parameters, respectively.
5. The method according to claim 4, wherein the step 33) specifically includes:
by solving equation (2), the optimal interference waveform of the airborne electronic interference system
Figure FDA0002902809550000031
Can be expressed as:
Figure FDA0002902809550000032
ξ*is a constant whose magnitude depends on a given MI threshold:
Figure FDA0002902809550000033
through dichotomy iterative computation, xi satisfying the formula (4)*The value is substituted into the formula (3) to obtain a group of interference waveforms which minimize the total transmitting power of the airborne electronic interference system
Figure FDA0002902809550000034
And finally determining the total interference power of the system.
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